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Quiz 7.1 & 7.2 – LT #46-47
AP Statistics @ BPI
Name:
LT #46: Distinguish between a parameter and statistic and distinguish the distribution of a population,
the distribution of a sample, and the sampling distribution of a statistic. Describe the
relationship between sample size and the variability of a statistic.
LT #47: I can describe and calculate probabilities from the sampling distribution of a sample
proportion, including checking all appropriate conditions.
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1. For each description below, identify the population and the parameter of interest, as well as the sample and
the statistic of interest. Make sure to use correct notation for the parameter and statistic.
(a) A 1993 survey conducted by the Richmond Times-Dispatch one week before election day asked 1200
voters which candidate for the state’s attorney general they would vote for. 37% of the respondents said
they would vote for the Democratic candidate. On election day, 41% of Virginia voters actually voted for the
Democratic candidate.
Population:
Sample:
Parameter:
Statistic:
(b) The National Center for Health Statistics reports that the mean systolic blood pressure for males 35 to 44
years of age is 128. The medical director of a large company looks at the medical records of 72 executives
in this age group and finds that the mean systolic blood pressure for these executives is 126.07.
Population:
Sample:
Parameter:
Statistic:
2. Suppose that in a certain community, 40% of the residents would answer “Yes” to the question, “Do you
know the names of at least five other people who live on your block?” Suppose you plan to take a random
sample of 100 people from this community and calculate the proportion of people in your sample whose
response to this question is “Yes”.
If you took a sample of 50 individuals instead of 100 from the original community, would the sampling
distribution of the statistic change? In what way? (Do not do any calculations – just explain.)
3. George is a big fan of music from the 1960s, and 26% of the songs on his smartphone are Beatles songs.
Suppose George sets his mp3 player to “shuffle,” so that it selects songs randomly (assume the shuffle
function permits repetition of songs, so the “population” of songs is essentially infinite). During a long drive,
George plays 50 randomly-selected songs.
(a) What is the sampling distribution of the sample proportion of Beatles songs during the long drive?
(b) Calculate the probability that more than 30% of the 50 randomly-selected songs are Beatles songs.